You are correct, when using the two-weapon fighting combat option, the Shield Master feat means any attacks you make with a shield are made at no penalty. Since all of your attacks are made with a shield, none of them are penalized. The Two-Weapon Fighting feat is irrelevant, since all that does is reduce those penalties, while Shield Master eliminates them.
Note that, normally, Shield Master also requires the Two-Weapon Fighting feat. That means you cannot use Shield Master without the Two-Weapon Fighting feat, as feats’ requirements must be met in order to use them.
But if you use a slayer talent to get a ranger combat style, and choose from the “weapon and shield” combat style in order to get Shield Master without meeting its prerequisites, then yes, you get to skip the Two-Weapon Fighting feat, and it won’t matter since all it does is reduce the penalties that you’re ignoring. Note that this approach does prevent you from taking Improved Two-Weapon Fighting and Greater Two-Weapon Fighting, which could be painful. You’ll have to think long and hard about whether or not it’s worth it to burn two or three feats on one or two extra attacks at low attack bonuses.
You only remove the penalties on shield attacks
Your understanding of the FAQ on the second answer is wrong, it says it removes the penalties when attacking with a shield, not when attacking while wielding/wearing a shield. To clarify, let me quote it again:
Shield Master: When Shield Master says “You do not suffer any penalties on attack rolls made with a shield while you are wielding another weapon” it seems like in context it means you don’t take the penalty for Two-Weapon Fighting, but it just says “any penalties” so it isn’t clear. Which penalties does the feat let a character ignore?
Shield Master allows a character to ignore the Two-Weapon Fighting penalties on attack rolls with a shield while wielding another weapon, but not any other penalties.
When you are attacking with a longsword, you are not attacking with a shield. Those are separate weapons and separate attacks, so the Two-Weapon Fighting penalties apply normally to your longsword attacks, but not your shield attacks (thanks to Shield Master).
This was clarified by Jason Bulmahn (Lead Designer back then) before that FAQ and the feat errata, which said:
Does Shield Mastery remove the penalties for all attacks if you are using a non-shield weapon and a shield and two-weapon fighting? Or does it only remove the penalties for the shield attack?
Shield Mastery only removes the penalty for Two Weapon Fighting on the Shield Bash itself, it does not remove it for a non-Shield weapon in your other hand.
This is only quoted here and there, but the actual link to that was actually broken sometime when Paizo upgraded their website in the past decade, so there are no direct links to this quote, and it cannot be found when searching their website. So, I believe this was archived or deleted and can no longer be found.
Best Answer
By strict rules as written, you are correct. The feat is written poorly and has been discussed ad nauseum on the official Paizo forums, with many folks arguing both sides. There are two factors to consider that allow you to clarify the intent of the feat.
First, removing all penalties to hit provides an overly large benefit in comparison to other feats. Most GMs would agree that this is clearly out of line and would not read the feat this way or allow players to use it in this fashion.
Second, (and perhaps more importantly) there is a feat table in the Pathfinder RPG Core Rulebook where this feat was originally printed. I've provided a tiny excerpt of the table below, where the Shield Master feat is listed (pg 116 in the 5th printing). You'll note that the condensed benefit for the feat is listed as "No two-weapon penalties when attacking with a shield". While this benefit description is by no means the be-all-end-all rules source for the feat, it does clarify the intent of the author.
For the two reasons above, it is likely that this feat was only intended to remove the two-weapon penalties when attacking with a shield along with another weapon (options 2 and 5 from your list above).
EDIT: Thanks to SevenSidedDie for bringing to attention the fact that we also now have an official FAQ Answer on this topic which reads: